Trunking system



March l0. 1925.

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UNITED STATESV PATENT .0FFlCE.

EDWARD c. MOLINA, or EAST ORANGE, NEW JERSEY, AssIeNOR 'ro AMERICAN TELE- PHONE ANI? TELEGRAPH COMPANY, A CORPORATION or NEW YORK.

TRUNRING sYs'rEir.

Application illed February 26, 1921. Serial No. l447,966.

v means for trunking between different subscribers in a telephone exchange or between subscribers in different exchanges.

' the traic.

Heretofore in providing trunking arrangements for handling the traflic originated by subscribers lines, particularly where the connections were established by means of switching machinery, two general methods have been proposed. One method involved providing a suificient number of trunks to handle all of the traffic originated by the subscribers lines involvedv and establishing connections between the calling sub- Scribers lines and the trunks through a switching arrangement, equipped with a number of selecting points corresponding to the number of trunks necessary to handle The other method consists in dividing the subscribers lines into groups and providing trunks for each group suicient in number to handle the traiiic originating in the group.

The first of these methods possesses the advantage that the total number of trunks necessary to handle the traiflc without an unduly large probability of a call being lost due to all of the trunks being busy will be a minimum. The method is subject to the serious disadvantage, however, that each subscriber must. have available a switching arrangement having a number of switching terminals sufficient to connect with each and all of the trunks, and where the traic is so large as to require a great number of trunks the expense involved in providing Ia switching arrangement having the necessary capacity#A becomes prohibitive.

The advantage of the second method is that the subscribers groups may be made sufficiently small so that the number of trunks necessary to handle the traiiic originatin in each group will be within the capacity limits of a relatively small and inexpensive switching arrangement; that is, a .switching arrangement having a com aratively small number of terminal points. This method is subject to the disadvantage, however, .that while economic in the matter of switching arrangements or machinery it is prodigal in the use of trunks, since the total number of trunks required to handle the traic from all of the subscribers is greater than would be the case in the irst methodreferred to above, due to the -fact that the ratio of trunks to subscribers varies inversely'with the number of subscribers having access to the trunks.

Itis one of the principal objects of the present invention to provide a scheme for multipling trunks such that the use of switches having a small number of switching points will be permitted without requiring a large ratio of the total number of trunks to the total number of subscribers.

The above object, as well as other objects more fully appearing hereinafter, are

accomplished by the use of what is herein termed a random slip multiple. The nature of this multiple will now be clear from the following description of the invention when read in connection with the accom- -panying drawing, Fig. 1 of which is a carrying the traffic originated by subscribers lines. YAssume that each subscribers line is equi pedwith a 100 point selector, thereby giving each line access to the enare 10o trunks. La the Order in which the trunks are connected to the different s'elec,

advantages previously discussed. Let us' now calculate for such a promiscuously congroup ot 20 trunks.

uected multiple the probability that more than 20 terminals (for example) will have to be hunted over by a selector before an idle trunk is obtained. The load to be carried may be adjusted so that the probability comes out any desired value as, for example, .001. It is evident that under these conditions the last S0 terminals of every group may be disconnected from the trunks without appreciably changing the eiiciency of the group of 100 trunks. Consequently each partially wired selector may be replaced by a 20 polnt switch having access to the same trunks in the same order as the lirst 20 trunks hunted over by the corresponding 100 point selector. Such an arrangement will involve what is herein termed a random slip multiple and has the obvious advantage that a 20 point switch may be used having access to 20 trunks previously selected at random from the total number of trunks without increasing the total number of trunks required to handle the traffic from all of the subscribers.

Considering the same arrangement from another view point, assume 5 independentgroups of lines equipped with selectors. Let each group of selecto-rs be wired to a The total number of trunks required will therefore be 100. If

. We bring together these isolated groups of selectors and groups of trunks by a partial interchange of trunks, or in other words, by arranging matters so that each one of the 5 groups or' selectors exchanges some of its trunks for some of the trunks assigned to each of the other 4 groups, we will have a promiscuously connected multiple of 100 trunks to some 20 of which each selector will have access. If this interchanging were done thoroughly the load carried by the total number of trunks with a given probability of lost calls would beappreciably greater than the load carried by the same number of trunks when divided into tive isolated groups each of which is accessible to a 20 point selector.

In order that the advantages inherent in the random slip multiple may be more apparent a .mathematical solution of the problem involved will now be given, The problem may be stated as follows:

A group of T trunks handles the traiic i originated by n sub-groups of lines or switches. A

Sub-group #l of lines or switches has access to a specified number t1 of the T trunks.

Sub-group #2 of lines or switches has access to a specified number t2 of the T trunks. Some of these t2 trunks are not included in the t] trunks assigned to sub-group #1.

Sub-group #3 of lines or switches has access to a speciied'number t3 of the T trunks. Some of these t3 trunks are not included in the t1 trunks assigned to subgroup #1 and some are not included in the t2 trunks assigned to sub-group #2. The trunks t1 and t2 together may, however, include all the t3 trunks.

Sub-group #a of lines or switches has access to a specified number tn of the T trunks. These tn trunks are not identical with either the t1, t2, t. or la1 trunks but they are all included in the totality of tft-152+ -l-t 1 trunks.

Thus, no sub-group of lines or switches has the exclusive use of a set of trunks chosen from among the T trunks and on the other hand no two or more sub-groups use identically the same trunks.

It is not assumed above that numerically tiza-:t3: tn 'lztn although this will probably be the case in practice.

Such a group of T trunks giving servicel to several over-lapping or inter-linking subgroups of lines, each of which sub-groups makes partial use of the T trunks, may be defined as a random slip multiple provided the following statement can be made with reference to it-when S of the T trunks are busy they are as likely to be one specified set of S trunks as another specified set of S trunks.

In order to solve this problem let PL: probability that a subscriber originating a call from a sub-group having access to t ot' T trunks fails to get an idle trunk.

Assume that at the moment the call is made S of the T trunks are busy. The probability of the existence of this assumed condition iS Asa-A where A is the average load carried by the group T.

The probability that the assumed S busy trunks embrace the particular t trunks to Therefore, the compound probability that S of the T trunks are busy and that these S trunks include the t trunks under consideration 1s A=e^ LS /T-t) A /T-t Awe-e L S'* LT i @j Therefore At` T lt S-T-x As-tei-A 'ftd-f r N E (rf t )+1 TA s t Where i A Ar Anl AN: i

P(T,A)=8 ad lllllltum] `probability that all T trunks are busy.

Now l hand, in a case where but one group is inp 'r-1 'r-z-i volved and the average load is 8.96, 20 Xs-te"A AxeA senders will be required in both cases and 7m: TX-:174) (TtA) the random slip multi le represents no PF-Tr- The preceding equation gives the probam bility of lost calls in terms of the average load carried by the roup oftrunks, the total number of trun s involved, and the number of trunks assigned to each gIroup. With this equation as a basis Tables and 1I have been prepared to show the saving involved in a random slip multiple as ycompared with a strai ht mult1ple,f that is, a multiple in whic the trunks are divided into independent groups5 p each 2G group accessible to a switch having a correspondingly small number of terminal points.

In a system wherepoint sender selec tors give access to the senders of an automatic switching exchange the saving in senders when the random slip arrangement is used instead of the straight .multiple will-be as indicated in Table I.'

It can be readily seen from the table that with the random slip arrangement of the number of senders required to carry a given loadk is considerably smaller than the number ofsenders necessary for the same load with the straight multi le.

probability of lost calls is .001 and the trunks are divided into ten groups of 20 each the random slip? -multiple arrangement will require only 137 senders 'as against 200 senders required by the straight multiple arrangement for an average load of 89.6, '28g the yexpression average load being here taken to mean the average number of connections existing at any one time for the 4'5 entire groupof trunks. The saving just regferred-to amounts to 31.5%. On the other For eX- .35 ample, it is apparent that i the allowable advantages over the stralght multiple, as in this limiting case the random slip multiple becomes a straight multiple.

Table II shows the saving in final switches which would result from a random arrangement of trunks to iinals in a panel system where the incoming multiple is divided into groups of 24 trunks each. Here also a smaller number of switches can carry the same load as a larger number with the straight multiple or inversely, the same number of switches in the random arrangement can take care of a larger load than in the straight multiple arrangement.

Table I.

' Random Straight multiple. multipla Per cent Average load. Savin in PTlb' Number Total Total sendeigrs. abmy' v of senders senders groups. required. required.

Table u.v

i Random Straight multlple. multiple I Percent Average load. savingin P-rb Number Total Total anais. bmwct finals nals groups. required. required.

1 a4 24 o 2 48 43 10.4 3 72 60 16.7 4 96 l 78 18.8 5 120 96 20.0

It is obvious, of course, that multiple arrangements involving the random slip principle may be embodied in various forms. In Figs. 2 and 3 are shown perfect random slips based on all of the 24 possible permutations of the numbers 1, 2, 3 and 4, the permutations being shown in Fig. 1, which illustrates in schematic form the permutations of four trunks taken four at a time in accordance with the first method outlined at the beginning of this specification. In all three figures a group of T=4 trunks is shown, together with n:24 sub-groups of subscribers lines. Each sub-group is represented by one line equipped with a selector giving the line access to four trunks inthe case of Fig. 1, three trunks in the case of Fig. 2 and -two trunks inthe case of Fig. 3. In Fig. 1 and the succeeding figures the arrows may therefore be taken to rep-resent the wipers of the switches, each of which is available to one or more subscribers and each switch having terminal points equal in number to the vertical lines connecting the arc of a circle representing the contact points of the switch with the horizontal lines representing the trunks. The numbers below the arrows representing the wipers of the switch indicate the order in which the switches obtain access to the trunks.

If, in the case of the arrangement of Fig. 1 a determination is made of the probability that more than 3 terminals will have to be hunted over by a selector before an idle trunk is obtained, and it be found that this probability is within the allowable probability of lost calls, the connection leading to the last trunk selected by each switch may be omitted from the switches in Fig. 1, in which case we get the perfect random slip arrangement o Fig. 2, which is based upon permutations of 4 trunks taken 3 at a time.

Similarly, if it be found that the allowable probability will permit of dispensing with connections to the last two trunks selected by each switch in Fig. 1, we may obtain the perfect random slip multiple illustrated in Fig. 3 which involves permutations of 4` trunks taken two at a time. It will be observed that in this instance each pair of adjacent sub-groups has access to the same two trunks and in the same order. This permits of modifying the cabling between the switches and the trunks as illustrated in Fig. 4.

Fig. 5 shows a random arrangement in which each sub-group of lines has access to 15:3, out of a total of T=5 trunks. This arrangement is obtained by taking every permutation of five things, three at a time. The break between the two halves of the figure indicates that a part of the permutations or possible connections is not illustrated, owing to lack of space. Assuming that the ermutations are worked out in logical or er, the connections shown at the left represent a small roup of permutations beginning with the rst, and the connections at the right indicate a similar group ending with the last permutation of the series.

The slip arrangements illustrated in Figs. 2, 3, 4 and 5 are based upon all possible permutations of the numbers involved. Consequently, each of these slips is a perfect random slip, since obviously no particular set of trunks is more likely to be busy than any other set involving an equal number of trunks. In practice, however, it would not be feasible to use slip arrangements based on all possible permuta-tions, where the total number of trunks T is large. For example, a slip multiple of T=25 trunks, in which each line is equipped with a z5 points selector would require the lines to be divided into 25 X 24 X 23 X 22 X 21=6,375,600 subgroups if every possible permutation of 25 things taken 5 at a time is to appear. It therefore becomes desirable to devise a system in which only a part of all of the possible permutations will be used and in which the selected permutations will be so chosen that no particular set of rtrunks is more likely to be busy than any other set involving the same number of trunks. In selecting a limited number of the total possible permutations, it is preferable to select a minimum amount of overlapping i. e. permutations such that any -trunks having a given number will appear in as few chosen permutations as possible.

Figs. 6, 7 and 8 illustrate practical forms of slip arrangements obtained by following the principles just discussed and in which a very thorough intermixture of trunks is obtained without dividing the lines into an abnormal number of sub-groups. Fig. 6, for example, shows what is herein termed a triangular islip arrangement in which T, the total number of trunks, is l5, and each selector is provided with tive points. The first sub-group of lines to the left has assigned to it trunks numbered 1, 3, 6, 10 and 15, and the selector points corresponding to these points will be selected in the order stated. These particular numbers are technically known as triangular numbers because they belong to the series of vnumbers which indicate the number of balls in successive layers (counting from the top) in a triangular pile of cannon balls. The numbersof the trunks to be assigned to the other groups are obtained by writing the numbers from 2 to 15 as the numbers of the first trunks to be selected by the groups to the right of that having assi ed to it the numbers 1, 3, 6, 10 andl 15. imilarly, the numbers of the second set of trunks to be selected is obtained by writing successive numbers beginning with 4, while the third set is obtained by writing successive numbers beginning with 7, etc. In each instance, when the number 15 is reached, the succeeding number will be V1. An analysis vof this trunk arrangement shows that while it is not a perfect random slip arrangement, it conforms very closely to the 8:23 and 16:24. As in the previous case,

the trunks to be assigned tothe other subgroups are determined by writing numbers consecutively from left to right.- This ar-4 rangement also substantially satisfies the requirements of the random slip multiple, although it is not a'perfect random type.

Fig. 8 shows a slip arrangement which,Y

for want of a better term, will be referred to as the arri-symmetric slip. At the left of the diagram 6 sub-groups of lines are indicated, each having access to 5 out of a total of 15 trunks. T o bring out more clearl which set of 5 trunks is to be assigne to each sub-group of lines, a diag- ,onal set of 6 zeros has been added to the 6 sets of 5 numbers. As will be readily seen, the 'arrangement of the numbers is such that the num'bers upon either side of an axis drawn through the series of zeros will be symmetrical with respect to `each other, hence the term axi-symmetric. An analysis of' the arrangement shown at the left of the diagram indicates that this portion of the system, standing by itself, will not conform to the requirements of a random slip, as certain trunks would obviously bel used otener than others. For example, trunk No. 1 is only accessible by lines in the first 2 groups, but is first choice for those particular groups. Upon the other hand, trunk No. 15 is accessible only to lines ofthe last 2 of the 6 groups, but is the last choice of those groups. Trunk No. 15, would, therefore, not be likely to be as busy as trunk 1. This difficulty is overcome, however, by providing additional groups as shown at the right-hand side of the diagram, these groups employing the same trunk numbers, but in inverse order. Therefore, trunk No. Y15 is first vchoice in 2 groups and last choice in 2 other groups, while the same'thing holds true of trunk No. 1. This arrangement as illustrated pro# vides for 12 grou s. Additional groups may be arranged or by' providing additional sets of 6 groups in which a still different order of selection will be used. For

example, the first sub-group of another set `.a1'ranged about `the zero axis.

, the

of 6 might employ the trunk numbers 5, 3, 1, 4 a-nd 2 in the order given. The numbers of the last choice of trunks of the other 5 sub-groups would then be 2, 4, 1, 3 and 5.

The remaining trunk numbers might be arranged just as shown at the left of Fig. 8, or they might be varied in their order as desired, so long as they are vsymmetrically This arrangement also. possesses substantially all the advantages of the perfect random slip multiple and provides a simple scheme for choosing the permutations to be used.

It will be obvious that the general principles herein disclosed may be embodied in many other organizations widely ldifferent from those illustrated without departing from the spirit of the invention as defined in the following claims.

What is claimed is:

1. A trunking system-in which a plurality ofV trunks are provided for handling the traffic originating from all of the subscribers lines involved, the subscribers lines being divided into subgroups each havino' access to a number of trunks less than the total ,number provided, the trunks assigned to the several sub-groups being interchanged so that the sub-groups overlap eachother and the' order of the selection of the trunks in the various sub-groups and the overlapping of oups eing such that when a given num er of the total number of trunks involved are busy, the busy trunks are at least approximately as likely to be one set of trunks of the given number as any other set of trunks of equal number.

2. A trunking system in which a plurality of trunks give service to several overlapping and interlinked sub-groups of lines, each sub-group of lines having access to a part only of the total number of trunks and the numbers of the trunks assigned to the subgroups and the order in which the numbers are selected being such that when a given numberof the total number of vtrunks are busy, the probability of one set of trunks of the given number being busyy will be at least approximately the vsame as the'probability that any other set of equal number will be busy.

3. A trunking system in which a plurality of trunks give service to several overlapping .and linterlinked sub-groups of lines, each sub-group of lines having access to a part only of the total number of trunks and the numbers of the trunks assigned to veach subgroup of a set of sub-groups being so chosen that they will fall into an axi-symmetric arrangement.

4. A trunking system in which a plurality of trunks ive service to several overlappin and inter inked sub-groups of lines, eac sub-grou of lines having access to a part only of e `total number of trunks and the 5. A trunking system in which a plurality y of trunks give service to several overlapping and interlinked sub-groups of lines, each sub-groupof lines having access to a part only of the total number of trunks, the subgroups being arranged in sets, the numbers of the trunks assigned to each sub-group of one set and their order of selection being such that the numbers will fall into an axisymmetric arrangement, and the numbers assigned to the sub-groups of other sets bemg s1m1larlyl arranged but their order of l selection being changed so that when a given number of the total number of trunks is busy, the probability of one set of trunks of the given number being busy will be at least approximatel the same as the probability that any ot, er set of equal number will be busy.

In testimony whereof, I have signed myA name to this speciication this 23rd day of February,r 1921.

EDWARD c. MOLINA. 

